SOLUTION: When you have to "Solve each system by graphing" on these two equations. How do you know what to multiply each side of the equation by. How do you know what number will work to sol

Question 58784: When you have to "Solve each system by graphing" on these two equations. How do you know what to multiply each side of the equation by. How do you know what number will work to solve and get the ordered pairs? I have this example:
2x + y + 2
2x + y + 8. I am to Solve each system by graphing.
thank you.
Answer by funmath(2933) (Show Source): You can put this solution on YOUR website!
When you have to "Solve each system by graphing" on these two equations.
2x + y + 2
2x + y + 8
You mistyped your equations, I am going to let the second + be =
L1) 2x+y=2
L2) 2x+y=8
If this is the case the system has no solution, because the lines are parallel.
You can pick any numbers you want to garph the lines. Often times if a line is written in standard form as these are, the intercept method is easy to use.
:
For L1) let x=0 and solve for y, this is the y-intercept (where the line crosses the y axis):
2(0)+y=2
0+y=2
y=2 Plot (0,2)
Now let y=0 and solve for x, this is the x intercept (where the line crosses the x-axis)
2x+(0)=2
2x=2
2x/2=2/2
x=1 Plot (1,0)
Connect the poinst and you have this line:

For L2) follow the same procedure:
Let x-0 and solve for y:
2(0)+y=8
0+y=8
y=8 Plot (0,8) The y-intercept
Now let y=0 and solve for x:
2x+0=8
2x=8
2x/2=8/2
x=4 Plot (4,0) the x-intercept
Connect the points and you have a second line:

As you can see the lines a parallel and will never intersect. There is no solution.
Happy Calculating!!!

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